$2$

$\text{'}e$

$(centerison$ zaxis$)$

Consider the above curve, which ends on $xz$ plane. For this curve and vector field of $\frac{?}{\text{b}\text{a}\text{r}}(A)=$yhat$(a{)}_x-$xhat$(a{)}_y+(xy-z)hat(a{)}_z,$ find the vector line integral of $\frac{{\displaystyle \underset{L}{\overset{\phantom{}}{}}}}{b}ar(A)*\frac{d}{b}ar(l)=?$

Hint: Cylindrical coordinate system can give much simpler solution.